(ATBD) SMAP Level 1 Radar Data Products - NASA

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adpative floating point quantizer (BFPQ) algorithm [9] to 4 bit samples with 5 bit
exponents generated for each block of 32 samples in a receive window. Depending
on PRI, the number of these 32-sample blocks varies from 9 to 14. These parameters
are selected to reduce data volume while still meeting the overall error budget. The
L1C processor will decode the BFPQ samples on the fly as data are processed.
The algorithm is designed to have unity gain and should not introduce any bias for
normal data with gaussian error statistics. RFI contamination can change this and
will require a bias correction described later.
7.4 Geometry Processing and Interpolation
SAR processing needs certain key geometric information to form the matched filters
and to calibrate the output image pixels. Some geometry processing can be
pre-computed by the L1C processor with results stored either in memory or in an intermediate
file. The key values will be the range and Doppler and their time derivatives
at the center of each output grid cell on the current SCH reference sphere. The
range R to a given position ⃗r on the surface is given by (26), and the Doppler shift
of a target at ⃗r is
f Dc = ( −2
λR )(⃗v sc · (⃗r sc − ⃗r)) (33)
Earth fixed coordinates are used to automatically account for the effects of Earth
rotation. For calibration, the attitude transformation matrix from Earth fixed coordinates
to beam pattern coordinates which rotate with the antenna will be needed
to determine the antenna gain correction. These values computed at some coarse
spacing by the L1C processor will then be interpolated to the individual pulse and
sample times needed for range and azimuth compression.
7.5 Range Compression
Range compression consists of the convolution of each range line with the complex
conjugate of the pulse form (in the frequency-domain). The range reference
function is calculated in the time-domain using the pulse form characteristics (pulse
bandwidth, pulse duration, sampling frequency) given by the radar instrument team,
and is transformed to the frequency domain using a FFT. A user-defined window
can also be applied to reduce the sidelobes of the impulse response in range. For
each range sample, timing is transformed into slant range, taking into account a
possible sample timing offset. Slant range values stay the same as long as the PRF
and reception window timing remain constant, which is assumed to be the case for
a full antenna scan. Loopback trap data provide a periodic sampling of the actual
transmit pulse waveform, and it may prove advantageous to use this measurement as